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There are 3 parts to this problem. Consider her Mom has not gifted anything
Part 1: $1000 investment for 17 quarters
Final value, A = P[(1+i)^n-1] * (1+i)/i
P = amount invested per quarter = $4000
i = cpmoundaded rate of interest = (4/100) /4 = 0.01 [divided by 4 because compounded quarterly]
n = 17
Hence , A = $18,430.44
Part 2: Final Value found in part 1 (A) kept for remaining 3 quarters
Final value, B = P(1+i)^n ,
here P = $18,430.44
i = 0.1
n = 3
Hence B = $18,988.45
Part 3: Final Value found of quarterly $1000 investment for last 2 quarters
Final value, C= P[(1+i)^n-1] * (1+i)/i
P = amount invested per quarter = $4000
i = cpmoundaded rate of interest = (4/100) /4 = 0.01 [divided by 4 because compounded quarterly]
n = 2
Hence , C = $2,010.00
Total value without her MOm's contribution would have been B+C = $18,988.45 + $2,010.00 = $20,998.45
So her Mom's gift is of value ($22,019 - $20,998.45) = $1020.55. This is final value of her mom's gift at the end of 5th year